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April 2014 10 (iv)

J

Janboyd

Member
Please may someone explain how you calculate total amount of interest paid over the term of the loan?
 
Not looked at the question but it's total repayments less the initial loan (since all repayments must end of covering the loan and the interest).
 
Oh sorry, I mean how are the total repayments calculated?

A loan of £20,000 is repayable by an annuity payable annually in arrear for 25 years.
The annual repayment is calculated at an effective interest rate of 8% per annum and increases by £50 each year.

25x1462.31 + (24x25)/2 x50
 
You can use arithmetic progression
N/2(A+L)
L= A+(N-1)D
25/2(1462.31+1462.31+24*50)=51557.75

Total interest paid =
51557.75-20000=31557.57
 
I don't understand why it isn't 25x1462.31 + (25x26)/2 x50
 
The Series is:
A, A+50, A+100, A+150 ,........,A+24*50

This may be rewritten as a sum of two series:
1) A, A, A..... upto 25 Terms
2) 50, 100, 150, 200.... upto 24 terms

Therefore the Sum would be

1) A*25
2) 24*25/2*50 The second series with 50 has only 24 terms: n*(n+1)/2
 
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